Mathematical Induction, topic 7.4 in the NSW Board of Studies Mathematics Extension 1 Syllabus, is difficult conceptual. I suspect students think there is a bit of smoke and mirrors happening. One introduction that I use, I first saw in a resource by Stuart Palmer. The same story appears in this article online: Mathematical Induction (PDF 92KB), Helen Bush, Reflections August 1992 sourced on NSWHSC Online.

INTRODUCTION: STORYTIME
A budgie flew in the window of the classroom and landed on Grant’s shoulder, turned to the class and
said: If I’m blue, then the next budgie that flies in the window is blue.
Another budgie flew in the window of the classroom and landed on Rachel’s shoulder, turned to the
class and said: If I’m blue, then the next budgie that flies in the window is blue.
Another budgie flew in the window of the classroom and landed on Matthew’s shoulder, turned to the
class and said: If I’m blue, then the next budgie that flies in the window is blue.
And this continued.
(All these budgies have been trained to talk and they all tell the truth.)Discussion: Are all the budgies blue ?

Here’s a little resource to aid this story. I think the budgie picture is sourced from Stuart Palmer.

(Right-click to save the full-size animated gif) Also download as a swf file, or QuickTime movie: